To follow up on my blog # 11 regarding the study of Gold Price vs. Exchange Rate, it is interesting to consider the theory of Purchasing Power Parity (PPP) into the picture, since the PPP has been using US Dollar as the reference to determine the relative values of currencies.
As The Economist  has introduced the most famous example of PPP by using the Big Mac Index to be used as an index to determine the relative value of other items, the study here will be using the Big Mac Index from  from 7 (seven) different currencies and the average Gold Price from  from the year 2007 to 2011.
Table 1 : Big Mac Index  and Gold Price  from 2007 to 2011
The Big Mac Indexes shown in the below Graph are showing an increasing value for the past two years and the highest index is for Switzerland [CHF] whereas the lowest is for Hong Kong [HKD]. The trend line used is the 3rd Grade Polynomial Trend Line, as it was already used in the previous studies.
Figure 1 : The Big Mac Index from 2007 to 2011
As a comparison is the Graph of the Gold Price USD/Oz. from the same period and showing an increasing trend from the beginning as below:
Figure 2 : The Gold Price  from 2007 to 2011 with trend-lines
The selection criteria will be the same for all approaches, namely:
Data period from the year 2007 to 2011, using average values.
The 3rd Order Polynomial Trend Line and R2 coefficient
To convert the Big Mac Price to Ounce of Gold and see the trends
Analysis and Comparison of Alternatives
To compare the input data and graphs, the R2 coefficient comparison for the all Big Mac Indexes are very acceptable as well as the Gold Price Coefficient, as shown in the below table:
Table 2 : R2 coefficient Result for Big Mac Indexes and Gold Price
The R2 Coefficient for the Chinese Yuan [CNY] is the worse, since the graph is almost flat compared to others, whereas the US Dollar is on zero line as reference line for Over or Undervalue of the currencies.
Selection of the preferred alternatives
Converting the Big Mac Price to Ounce of Gold to see gives us the below table and graph:
Table 3 : Big Mac Price in Ounce of Gold, using average Gold Price USD/Oz.
Figure 3 : Big Mac Prices in Ounce of Gold, using average Gold Price USD/Oz. and their trend lines
Table 4 : R2 coefficient Result for Big Mac Prices in Oz of Gold
Comparing the trends in Figure 3 and the R2 Coefficients in Table 4, we can see that
The Big Mac Price for USA [USD] is no longer in zero line
For the next Period there are only three inclining trend lines namely for Switzerland [CH], Euro Based Countries [EUR] and Singapore [SGD]
For the next Period there are three declining trend lines for Indonesia [IDR], Hong Kong [HKD] and China [CNY]
Perfect R2 Coefficient for Big Mac Price in Gold for China [CNY] R2 = 1, compared to the worse in its Big Mac Index
All other R2 Coefficient are very acceptable, close to perfect trend.
Performance Monitoring & Post Evaluation of Results
From the above calculation and above analysis, we can say that:
To make the common approach of the 3rd Order Polynomial Tend Line to all set of selected data is the right approach and giving the very acceptable values.
Taking the Big Mac Index and convert the values to Gold Price is saying that the US Dollar has a different behavior and cannot be seen as the stable reference for the Index.
With the Gold Price reference, the trends vary for different currencies, and behave differently than if only considering the Big Mac Index as the Purchasing Power Parity application.
- Sullivan, William G., Wicks, Elin M. & Koelling, C. Patrick (1942), Engineering Economy 15th Edition, Singapore: Prentice Hall, Inc.
- Michael Bassard & Diane Riter (2010), The Memory Jogger 2nd Edition, Canada, GOAL/QPC
- XE, The World’s Favorite Currency Site http://www.xe.com/ucc/
- KITCO http://www.kitco.com/scripts/hist_charts/yearly_graphs.plx
- John K. Hollmann, PE CCE (2006), Total Cost Management Framework, A Process for Applying the Skills and Knowledge of Cost Engineering 1st Edition, USA, AACE International – The Association for the Advancement of Cost Engineering
- The Economist, http://www.economist.com/node/12991434?story_id=E1_TNJJTQPQ